Absolute Value Functions Flashcard

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, denoted as y = |x|.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

How does the transformation y = |x - 4| affect the graph of y = |x|?

Back

The transformation y = |x - 4| shifts the graph of y = |x| to the right by 4 units.

Front

What is the range of the absolute value function y = |x|?

Back

The range of y = |x| is y ≥ 0, meaning it includes all non-negative real numbers.

Front

How do you find the vertex of an absolute value function in the form y = a|x - h| + k?

Back

The vertex of the function is at the point (h, k).

Front

What is the vertex of the function y = |x - 2| + 5?

Back

The vertex of the function y = |x - 2| + 5 is (2, 5).

Front

What does the negative sign in front of an absolute value function indicate?

Back

The negative sign indicates that the graph is reflected over the x-axis.

Front

What is the vertex of the function y = -2|x + 4| - 3?

Back

The vertex of the function y = -2|x + 4| - 3 is (-4, -3).

Front

How does the coefficient in front of the absolute value affect the graph?

Back

The coefficient affects the vertical stretch or compression of the graph. A value greater than 1 stretches it, while a value between 0 and 1 compresses it.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, y = |x| + 3 shifts the graph up by 3 units.